sibl
Cross-Correlation
Introduction
The cross-correlation implements the following conceptual steps:
- Given two signals
- r(t) is the reference signal with bounds [r_a, r_b].
- s(t) is the subject signal with bounds [s_a, s_b].
- Synchronization:
- Find the global minimum T_a = min(r_a, s_a).
- Find the global maximum T_b = max(r_b, s_b).
- Construct a global time interval [T_a, T_b].
- Choose a global time step, DT, to be the minimum of the reference time step and the subject time step.
- Correlation:
- Keep the reference signal stationary. Move the subject signal along the t axis until the last data point of the subject signal is multiplied with the first data point of the reference signal.
- Then, slide the subject signal to the right on the t axis by DT, calculating the inner product of the two signals for each DT in [T_a, T_b].
- Find the largest value of the foregoing inner products, and then for that DT step, move the subject curve to align with the reference curve. This will represent the highest correlation between the reference and the signal.
Example:
- two triangular acceleration pulses, with
- time integration and
- cross-correlation
Input file: correlation_recipe.json
Outputs:
Error metrics:
- cross-correlation relative error: 33 percent
- L2-norm error rate: 102 percent
Example:
- sawtooth examples of Anomaly site
Input file: anomaly_recipe.json
Outputs:
Error metrics:
- cross-correlation relative error: 2.5 percent
- L2-norm error rate: 8.3 percent
Example: Unit test case.
- For more examples, see the unit test examples in test_correlation.py.